Local control of chaotic systems - A Lyapunov approach

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 7, 1998, Pages 1565-1573

  Richter, Hendrik ^b   Reinschke, Kurt J ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^b LEIPZIG UNIVERSITY OF APPLIED SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040944380     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498001212     Document Type: Article

References (20)

1. Chen, G. & Dong, X. [1993a] "From chaos to order - Perspectives and methodologies in controlling chaotic nonlinear dynamical systems," Int. J. Bifurcation and Chaos 3, 1363-1409.
2. Chen, G. & Dong, X. [1993b] "Controlling Chua's circuit," J. Circuits Syst. Comput. 3, 139-149.
3. Ditto, W. L., Spano, M. L. & Lindner, J. F. [1995] "Techniques for the control of chaos," Physica D86, 198-211.
4. Gantmakher, F. R. [1959] Theory of Matrices (Chelsea Publishing Co., NY)
5. Guckenheimer, J. & Holmes, P. [1986] Nonlinear Oscillation, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, NY).
6. Hahn, W. [1967] Stability of Motion (Springer-Verlag, Berlin).
7. Hoff, A. A., Diebner, H. H. & Baier, G. [1995] "Reversible control of chemical reaction systems," Z. Naturforsch. 50a, 1141-1146.
8. Holmes, P. J. [1979] "A nonlinear oscillator with a strange attractor," Philos. Trans. R. Soc. London A292, 419-448.
9. Kailath, T. [1980] Linear Systems (Prentice-Hall, Englewood Cliffs, NJ).
10. Nijmeijer, H. & van der Schaft, A. [1990] Nonlinear Dynamical Control Systems (Springer-Verlag, NY).
11. Nijmeijer, H. & Berghuis, H. [1995] "On Lyapunov control of the Duffing equations," IEEE Trans. CAS 42, 473-477.
12. Ott, E., Grebogi, C. & Yorke, J. A. [1990] "Controlling chaos," Phys. Rev. Lett. 64, 1196-1199.
13. Ott, E. [1993] Chaos in Dynamical Systems (Cambridge University Press, Cambridge, UK).
14. Paskota, M., Mees, A. I. & Teo, K. L. [1995] "On control of chaos: Higher periodic orbits," Dyn. Control 5, 365-387.
15. Paskota, M. [1996] "On local control of chaos: The neighbourhood size," Int. J. Bifurcation and Chaos 6, 169-178.
16. Powell, M. J. D. [1983] "Variable metric methods for constrained optimization," in Mathematical Programming: The State of the Art, eds. Bachern, A., Grötschel, M. & Korte, B. (Springer-Verlag, Berlin), pp. 288-311.
17. Romeiras, F. J., Grebogi, C., Ott, E. & Dayawansa, W. P. [1992] "Controlling chaotic dynamical systems," Physica D58, 165-192.
18. Shinbrot, T., Grebogi, C., Ott, E. & Yorke, J. A. [1993] "Using small perturbations to control chaos," Nature 363, 411-417.
19. Stoten D. P. & di Bernardo, M. [1996] "Application of the minimal control synthesis algorithm to the control and synchronization of chaotic systems," Int. J. Control 65, 925-938.
20. Wu, C. W. & Chua, L. O. [1994] "A unified approach to synchronization and control of dynamical systems," Int. J. Bifurcation and Chaos 4, 979-998.